THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

In the course of his stimulating and suggestive paper in your recent issue, No. ro, pp. 226–38, Mr. A. J. Potter writes on p. 233 “but there is no simple construction by which X can then be found”, and again on p. 237 “a direct construction, if there be such”. This cheerful challenge invites the construction of a circle centred on a given line, passing through a given point thereon, and touching a given circle, and I have found the lure of Mr. Potter's gauntlet as irresistible as its recovery has proved delicate. In order to shoulder responsibility and by no means to claim highly improbable originality, let me confess that the problem is new to me and the two constructions I offer are my own; I venture to hope that Mr. Potter may consider one or other of them not unworthy of his epithet “simple”, though I freely admit the aptitude of his empiric procedure to its purpose. The proofs are not long, but for fear of overshooting my welcome I offer them to anyone for the asking; and for the same reason my diagrams are small and therefore mere.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour.     

THE PRIMARY TRIANGULATION OF SARAWAK

Abstract

Historical.—When my predecessor, Mr N. A. Middlemas, was seconded from the Survey Department of Malaya in 1925, the survey framework of the State was technically negligible.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject.     

DISTORTING A NETWORK TO FIT CONTROL POINTS: AN ALTERNATIVE EXPRESSION FOR THE SCHOLS ADJUSTMENT

Abstract

Another form of Mr. Lauf's expression for a conformal adjustment of a system of coordinated points may be of interest. These are assumed to be already in harmony with i control points and are to be brought into agreement with j further points. (Mr. Lauf deals explicitly in his paper with the special case i = 2, j = 1, but he adumbrates a general solution.)     

DEVIATION OF THE VERTICAL. DISCUSSION

Abstract

The following is a report of the discussion on the paper by Mr. A. R. Robbins on “Deviation of the Vertical” which was read at a meeting of the Land Surveying Division of the Royal Institution of Chartered Surveyors held on Tuesday, 12th December, 1950, and which was published in the January issue of this Review (xi, 79, 28–36).     

ON THE ORTHOMORPHIC PROPERTY OF SCHOLS ADJUSTMENT

Abstract

In vol. iv, nos. 29 and 30, of the E.S.R., there appeared an article by Mr. D. R. Hendrikz on the “Adjustment of the Secondary Triangulation of South Africa”. He shows that, in applying the Schols method of orthomorphic transmission to the adjustment of a secondary net to a primary triangle, the secondary sides suffer small displacements.     

THE COLOURS QUESTION

Abstract

The foundation of my former paper was nothing more substantial than a recollection of reading or hearing long ago that the property of the four colours existed in practice but had never yielded to strict theoretical analysis. I am therefore most grateful to Col. G. S. C. Cooke and Mr. G. W. Ross Jackson for their letters to the Editor (vol. iii, no. 15, pp. 52–5) citing the relative authorities, as they enable me to locate and acknowledge my debt to Mr. W. W. Rouse Ball, whose book was certainly in my hands in the Oxford Union Library some forty years ago. I wish I could remember his demonstration of the problem, but my subconscious faculties seem, from what Col. Cooke says, to have evolved a tolerable imitation of it, and until I have an opportunity of seeing the book again or of consulting any of the other authorities, I shall rest content in the assurance that, wherever my arguments may differ in substance from those of Mr. Rouse Ball, my errors will be so flagrant as to deceive none but myself, though my serenity in this connexion is somewhat shaken by the fate that seems to have attended the first welcome efforts to unmask a few of them.     

THE TRANSVAAL-SOUTHERN RHODESIA GEODETIC CONNEXION

Abstract

In the original geodetic series in Southern Rhodesia—completed by Mr Alexander Simms in 1901—the geographical coordinates of all stations were referred to the point SALISBURYas origin. The coordinates of SALISBURY were fixed by interchange of telegraphic signals with the Royal Observatory at the Cape for longitude, combined with astronomical determinations of time, latitude, and azimuth (see Vol. III, “Geodetic Survey of South Africa”).     

RELAXATION AND THE CO-ORDINATE METHOD OF TRIANGULATION ADJUSTMENT

Abstract

Few, most certainly, will dispute the value of Mr Black's paper describing a method of “Systematic Relaxation”, which appeared in a previous number of this Review. At the same time, however, it seems to the writer to be only fair to readers to point out that the application of the method to triangulation adjustment is really a treatment, from a slightly different aspect, of methods that have long been established.     

THOUGHTS ON THE RUWANDIZ ROAD

Abstract

THE article on Road-Surveying in the East by Mr. J. N. List in the Empire Survey Review, No.6, 263–74, is well worthy of perusal. From the beginning, with his apt quotation from Kipling, to the end where he compares the text-book ideal of road location with the indifferent compromise amidst difficulties that the British engineer in the East is lucky to be able to achieve, I felt in accord with his observations. Having spent four years on a similar kind of work, I consider that this article well deserves the appreciation of its author's profession.     

INTERPOLATING FROM TRAVERSE TABLES TO SECONDS

Abstract

In the Empire Survey Review, no. 4, 1932, Mr. Clendinning has described a method of interpolating from traverse tables to seconds. Below is another method, due to Prof. Nekrassov, for use with traverse tables published by him. The method is described in The Geodezist, Moscow, 1936, no. I, pp. 47–52.     

A NOVEL METHOD OF MEASURING THE COEFFICIENT OF THERMAL EXPANSION OF INVAR

Abstract

In a letter published in a recent issue of Nature, Prof. L. F. Bates and Mr J. C. Wilson, of University College, Nottingham, have described a new and novel method of determining the coefficient of thermal expansion of invar. Although this method is hardly likely to be applied to the measurement of the coefficient of expansion of long invar tapes, such as are used by surveyors, yet it is so novel and ingenious in itself that a short reference to it may not be out of place in this Review. One extremely interesting thing about it is that no measurements of a length, or of changes of length, are involved.     

TRAVERSING WITH THEODOLITE AND CHAIN

Abstract

As Mr H. F. Rainsford (E.S.R., no. 37, vol. v, July 1940) says, the ordinary accurate survey traverse, through its “ordinariness,” has been neglected in the printed word. The technique—perfected by much practice—has been handed down by word of mouth only from father to son, from surveyor to pupil.     

CADASTRAL SURVEY AND LAND RECORDS

Abstract

We regret that, owing to illness and the pressure of other demands on them in the same field, it has been necessary to interrupt the publication of the papers on cadastral subjects which Sir Ernest Dowson and Mr. Sheppard are contributing to the Review. We hope, however, to resume this valuable and interesting series in the January 1947 issue.— ED., E.S.R.     

MAP REPRODUCTION IN THE TROPICS

Abstract

The useful paper on “Map Printing in Ceylon” which was written by Mr. W. S. Maddams of the Ceylon Survey Department for the 1935 Conference of Empire Survey Officers has been read with interest in the Gold Coast. The writer of the present note was not present at the Conference but has read the report of the discussion on that paper. It appears to him that Mr. Maddams makes certain generalizations, based on his own, experience in Ceylon, regarding map reproduction in the Tropics and, however true these statements may be as regards Ceylon, they certainly do not apply to the Gold Coast and probably not to some other tropical countries. As it is possible that another Colony, when starting a map-printing establishment of its own, might be led, on the strength of the paper read at the Conference, to believe that less expensive (though less elaborate) methods than those used in Ceylon are not possible in a tropical country, the following notes on the methods used and found successful in the Gold Coast may be of some value. They are not intended to be a criticism of Mr. Maddams' paper but only to supplement it with a record of experience obtained in another part of the world.